Breed family: Difference between revisions

Revision as of 05:39, 15 September 2023

The breed family of temperaments are rank-3 microtemperaments which temper out 2401/2400. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, the optimal patent val 2749et will certainly do the trick.

Breed

Subgroup: 2.3.5.7

Comma list: 2401/2400

Mapping: [⟨1 1 1 2], ⟨0 2 1 1], ⟨0 0 2 1]]

mapping generators: ~2, ~49/40, ~10/7

Mapping to lattice: [⟨0 2 -1 0], ⟨0 0 -2 -1]]

Lattice basis:

49/40 length = 0.7858, 8/7 length = 1.1241

Angle (49/40, 8/7) = 107.367°

Minimax tuning:

7- and 9-odd-limit eigenmonzo (unchanged-interval) basis: 2.3.5

Optimal ET sequence: 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d

Badness: 0.0153 × 10^-3

Projection pair: 3 = ~2401/800 to 2.5.7

Scales: breed11

Jove

Main article: Jove

Jove (formerly known as wonder) tempers out 243/242 and 441/440. Jove converts breed into an 11-limit temperament via 441/440, which equates 49/40 with 11/9, and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. 72, 130, 171 and 202 are good edos for jove.

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440

Mapping: [⟨1 1 1 2 2], ⟨0 2 1 1 5], ⟨0 0 2 1 0]]

Minimax tuning:

11-odd-limit eigenmonzo (unchanged-interval) basis: 2.7/5.11

Optimal ET sequence: 27e, 31, 41, 58, 72, 130, 202

Badness: 0.241 × 10^-3

Projection pairs: ~3 = ~242/81, ~5 = ~2200/441, ~7 = ~440/63, ~11 = ~644204/59049 to 2.7/5.11/9

Jovial

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 364/363, 441/440

Mapping: [⟨1 1 1 2 2 1], ⟨0 2 1 1 5 11], ⟨0 0 2 1 0 -1]]

Minimax tuning:

13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/5.13/9
15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7/5.15/13

Optimal ET sequence: 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e

Badness: 0.624 × 10^-3

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 243/242, 364/363, 441/440, 595/594

Mapping: [⟨1 1 1 2 2 1 3], ⟨0 2 1 1 5 11 9], ⟨0 0 2 1 0 -1 -3]]

Minimax tuning:

17-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.17/9

Optimal ET sequence: 27effg, 31fg, 41, 58, 72, 130, 171, 243

Badness: 0.741 × 10^-3

Jofur

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 196/195, 243/242

Mapping: [⟨1 1 1 2 2 4], ⟨0 2 1 1 5 -1], ⟨0 0 2 1 0 0]]

Optimal ET sequence: 27e, 31, 41, 58, 99ef, 157eff

Badness: 0.749 × 10^-3

Jovis

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 441/440

Mapping: [⟨1 1 1 2 2 2], ⟨0 2 1 1 5 -3], ⟨0 0 2 1 0 5]]

Optimal ET sequence: 27e, 31, 45ef, 58, 72, 103, 130, 233, 363

Badness: 0.542 × 10^-3

Agni

Subgroup: 2.3.5.7.11

Comma list: 385/384, 1375/1372

Mapping: [⟨1 1 1 2 5], ⟨0 2 1 1 0], ⟨0 0 2 1 -3]]

Mapping to lattice: [⟨0 2 1 1 0], ⟨0 0 2 1 -3]]

Lattice basis:

49/40 length = 0.756, 10/7 length = 0.819

Angle (49/40, 10/7) = 106.460 degrees

Minimax tuning:

11-odd-limit

[[1 0 0 0 0⟩, [0 1 0 0 0⟩, [23/10 3/10 2/5 0 -2/5⟩, [12/5 2/5 1/5 0 -1/5⟩, [23/10 3/10 -3/5 0 3/5⟩]

eigenmonzo (unchanged-interval) basis: 2.3.11/5

Optimal ET sequence: 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee

Badness: 0.494 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 625/624, 1375/1372

Mapping: [⟨1 1 1 2 5 -1], ⟨0 2 1 1 0 2], ⟨0 0 2 1 -3 8]]

Optimal ET sequence: 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff

Badness: 0.923 × 10^-3

Zisa

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 5632/5625

Mapping: [⟨1 1 1 2 -3], ⟨0 2 1 1 8], ⟨0 0 2 1 8]]

Optimal ET sequence: 31, 68e, 99e, 130, 239, 270, 670, 940, 1210, 2150c

Badness: 0.640 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 1716/1715, 4096/4095

Mapping: [⟨1 1 1 2 -3 7], ⟨0 2 1 1 8 -6], ⟨0 0 2 1 8 -3]]

Optimal ET sequence: 31, 78f, 99e, 109, 130, 239, 270, 571, 701, 841, 971, 1241

Badness: 0.830 × 10^-3

Baldur

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 9801/9800

Mapping: [⟨2 0 1 3 7], ⟨0 2 1 1 -2], ⟨0 0 2 1 3]]

mapping generators: ~99/70, ~343/198, ~10/7

Minimax tuning:

11-odd-limit

[[1 0 0 0 0⟩, [3/4 0 1/2 1/2 -1/2⟩, [0 0 1 0 0⟩, [23/16 0 5/8 1/8 -1/8⟩, [23/16 0 5/8 -7/8 7/8⟩]

eigenmonzo (unchanged-interval) basis: 2.5.11/7

Optimal ET sequence: 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de

Badness: 0.166 × 10^-3

Projection pairs: 2 9801/4900 3 117649/39204 7 9801/1400 11 913517247483640899/83082326424002500 to 5.7/2.99/4

Greenland

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 1716/1715

Mapping: [⟨2 0 1 3 7 -1], ⟨0 2 1 1 -2 4], ⟨0 0 2 1 3 2]]

Optimal ET sequence: 58, 72, 130, 198, 270, 940, 1210f

Badness: 0.433 × 10^-3

Complexity spectrum: 15/13, 7/5, 8/7, 7/6, 4/3, 15/14, 5/4, 18/13, 13/12, 14/13, 13/10, 6/5, 16/15, 11/10, 9/7, 9/8, 16/13, 10/9, 14/11, 11/8, 15/11, 12/11, 13/11, 11/9

Projection pairs: 2 19600/9801 3 676/225 5 10400/2079 7 20384000/2910897 11 19208000000000000/1750211597736459 13 5026736/385875 to 10/7.200/99.26/15

Freya

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3025/3024

Mapping: [⟨1 1 3 3 2], ⟨0 2 3 2 1], ⟨0 0 -4 -2 3]]

mapping generators: ~2, ~49/40, ~55/42

Minimax tuning:

11-odd-limit eigenmonzos (unchanged-intervals): 2, 14/11, 4/3

Optimal ET sequence: 31, 41, 72, 167, 188, 198, 239, 270, 342, 612, 954, 1566, 3101de, 3443de, 4055de, 4397cdee, 4667dee, 5009cddee

Badness: 0.170 × 10^-3

Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024 to 2.49/5.77/3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2401/2400, 3025/3024, 4096/4095

Mapping: [⟨1 1 3 3 2 4], ⟨0 2 3 2 1 -9], ⟨0 0 -4 -2 3 6]]

Optimal ET sequence: 31, 41, 72f, 198f, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615

Badness: 0.855 × 10^-3

Projection pairs: ~3 = ~2401/800, ~5 = ~22880495169/4575312500, ~7 = ~1058841/151250, ~11 = ~33275/3024, ~13 = ~1814078464000000000000000/139662717676432916098329 to 2.49/5.77/3

Eir

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2401/2400, 3025/3024

Mapping: [⟨1 1 3 3 2 0], ⟨0 2 3 2 1 6], ⟨0 0 -4 -2 3 5]]

Optimal ET sequence: 13cdf, 31f, 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f

Badness: 0.581 × 10^-3

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400

Mapping: [⟨1 1 3 3 2 0 7], ⟨0 2 3 2 1 6 6], ⟨0 0 -4 -2 3 5 -12]]

Optimal ET sequence: 41g, 72, 198g, 239f, 270, 311, 509, 581, 1234, 1815

Badness: 0.700 × 10^-3

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 1225/1224, 1540/1539, 2080/2079, 3136/3135, 4200/4199

Mapping: [⟨1 1 3 3 2 0 7 6], ⟨0 2 3 2 1 6 6 -2], ⟨0 0 -4 -2 3 5 -12 -3]]

Mapping generators: ~2, ~49/40, ~55/42

Optimal ET sequence: 41g, 72, 198g, 239f, 270, 311, 581, 1234, 1815

Badness: 0.692 × 10^-3

Heimlaug

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 1716/1715, 3025/3024

Mapping: [⟨1 1 3 3 2 7], ⟨0 2 3 2 1 6], ⟨0 0 -4 -2 3 -13]]

Optimal ET sequence: 8bcef, 15bbccdeeff, 23bcf, 31, 72, 103, 167, 198, 270, 571, 643, 913f

Badness: 0.601 × 10^-3

17-limit

Equave 10/7 and 16-note scales with that period are of interest.

Subgroup: 2.3.5.7.11.13.17

Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715

Mapping: [⟨1 1 3 3 2 7 7], ⟨0 2 3 2 1 6 6], ⟨0 0 -4 -2 3 -13 -12]]

mapping generators: ~2, ~49/40, ~17/13

Optimal ET sequence: 8bcefg, 15bbccdeeffggg, 23bcfg, 31, 64be, 72, 103, 167, 198g, 239, 270

Badness: 0.829 × 10^-3

Vili

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 391314/390625

Mapping: [⟨1 1 5 4 10], ⟨0 2 3 2 6], ⟨0 0 -6 -3 -14]]

Optimal ET sequence: 27e, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 670, 913, 1043, 1313, 1583

Badness: 1.26 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 1716/1715, 4225/4224

Mapping: [⟨1 1 5 4 10 4], ⟨0 2 3 2 6 1], ⟨0 0 -6 -3 -14 -1]]

Optimal ET sequence: 27e, 37, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 913f

Badness: 0.738 × 10^-3

Frigg

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 644204/643125

Mapping: [⟨1 1 3 3 4], ⟨0 2 3 2 4], ⟨0 0 -10 -5 -11]]

Optimal ET sequence: 45e, 58, 103, 161, 212, 270, 643, 913, 1183e

Badness: 1.79 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 1716/1715, 10648/10647

Mapping: [⟨1 1 3 3 4 5], ⟨0 2 3 2 4 3], ⟨0 0 -10 -5 -11 -14]]

Optimal ET sequence: 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef *

* optimal patent val: 1241

Badness: 0.934 × 10^-3

Ennealimmic

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 4375/4374

Mapping: [⟨9 1 1 12 0], ⟨0 2 3 2 0], ⟨0 0 0 0 1]]

mapping generators: ~27/25, ~5/3, ~11

Optimal ET sequence: 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd

Badness: 0.275 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2401/2400, 4375/4374

Mapping: [⟨9 1 1 12 0 -31], ⟨0 2 3 2 0 5], ⟨0 0 0 0 1 1]]

Optimal ET sequence: 27, 45f, 54cff, 72, 171, 198, 270, 639, 711, 981, 1692e

Badness: 0.755 × 10^-3

Breed family: Difference between revisions

Revision as of 05:39, 15 September 2023

Contents

Breed

Jove

Jovial

17-limit

Jofur

Jovis

Agni

13-limit

Zisa

13-limit

Baldur

Greenland

Freya

13-limit

Eir

17-limit

19-limit

Heimlaug

17-limit

Vili

13-limit

Frigg

13-limit

Ennealimmic

13-limit

Navigation menu

@@ Line 1: / Line 1: @@
-The '''breed family''' of temperaments are rank-3 microtemperaments which temper out [[2401/2400]]. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, the [[optimal patent val]] 2749et will certainly do the trick.
+The '''breed family''' of [[temperament]]s are [[Rank-3 temperament|rank-3]] [[microtemperament]]s which [[Tempering out|temper out]] [[2401/2400]]. While it is so accurate it hardly matters what is used to temper it, or whether it is tempered at all, the [[optimal patent val]] 2749et will certainly do the trick.
 == Breed ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 2401/2400
-[[Mapping]]: [{{val| 1 1 1 2 }}, {{val| 0 2 1 1 }}, {{val| 0 0 2 1 }}]
+{{Mapping|legend=1| 1 1 1 2 | 0 2 1 1 | 0 0 2 1 }}
-Mapping generators: ~2, ~49/40, ~10/7
+: mapping generators: ~2, ~49/40, ~10/7
 [[Mapping to lattice]]: [{{val| 0 2 -1 0 }}, {{val| 0 0 -2 -1 }}]
@@ Line 17: / Line 17: @@
 [[Minimax tuning]]:
-* 7- and [[9-odd-limit]] eigenmonzos (unchanged-intervals): 2, 6/5, 5/4
+* [[7-odd-limit|7-]] and [[9-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.5
 {{Optimal ET sequence|legend=1| 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d }}
@@ Line 28: / Line 28: @@
 == Jove ==
-{{main| Jove }}
+{{Main| Jove }}
-Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been deprecated as a name due to conflict with another temperament also given that name. Jove converts breed into an 11-limit temperament via 441/440, which equates 49/40 with 11/9, and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. 72, 130, 171 and 202 are good edos for jove.
+Jove (formerly known as wonder) tempers out 243/242 and 441/440. Jove converts breed into an 11-limit temperament via 441/440, which equates 49/40 with 11/9, and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. 72, 130, 171 and 202 are good edos for jove.
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 243/242, 441/440
-[[Mapping]]: [{{val| 1 1 1 2 2 }}, {{val| 0 2 1 1 5 }}, {{val| 0 0 2 1 0 }}]
+{{Mapping|legend=1| 1 1 1 2 2 | 0 2 1 1 5 | 0 0 2 1 0 }}
-Mapping generators: ~2, ~11/9, ~10/7
 [[Minimax tuning]]:
-* [[11-odd-limit]] eigenmonzos (unchanged-intervals): 2, 7/5, 11/8
+* [[11-odd-limit]] [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5.11
 {{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 72, 130, 202 }}
@@ Line 53: / Line 51: @@
 Comma list: 243/242, 364/363, 441/440
+Mapping: {{mapping| 1 1 1 2 2 1 | 0 2 1 1 5 11 | 0 0 2 1 0 -1 }}
 Minimax tuning:
-* 13-odd-limit eigenmonzos (unchanged-intervals): 2, 10/9, 13/10
+* 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/5.13/9
-* 15-odd-limit eigenmonzos (unchanged-intervals): 2, 15/13, 7/5
+* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7/5.15/13
-Mapping: [{{val| 1 1 1 2 2 1 }}, {{val| 0 2 1 1 5 11 }}, {{val| 0 0 2 1 0 -1 }}]
-Mapping generators: ~2, ~11/9, ~10/7
 {{Optimal ET sequence|legend=1| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}
@@ Line 71: / Line 67: @@
 Comma list: 243/242, 364/363, 441/440, 595/594
-Mapping: [{{val| 1 1 1 2 2 1 3 }}, {{val| 0 2 1 1 5 11 9 }}, {{val| 0 0 2 1 0 -1 -3 }}]
+Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 2 1 1 5 11 9 | 0 0 2 1 0 -1 -3 }}
-Mapping generators: ~2, ~11/9, ~10/7
 Minimax tuning:
-* 17-odd-limit eigenmonzos (unchanged-intervals): 2, 18/17, 6/5
+* 17-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.17/9
 {{Optimal ET sequence|legend=1| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}
@@ Line 87: / Line 81: @@
 Comma list: 144/143, 196/195, 243/242
-Mapping: [{{val| 1 1 1 2 2 4 }}, {{val| 0 2 1 1 5 -1 }}, {{val| 0 0 2 1 0 0 }}]
+Mapping: {{mapping| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }}
-Mapping generators: ~2, ~11/9, ~10/7
 {{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 99ef, 157eff }}
@@ Line 100: / Line 92: @@
 Comma list: 243/242, 351/350, 441/440
-Mapping: [{{val| 1 1 1 2 2 2 }}, {{val| 0 2 1 1 5 -3 }}, {{val| 0 0 2 1 0 5 }}]
+Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}
-Mapping generators: ~2, ~11/9, ~10/7
 {{Optimal ET sequence|legend=1| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}
@@ Line 109: / Line 99: @@
 == Agni ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 385/384, 1375/1372
-[[Mapping]]: [{{val| 1 1 1 2 5 }}, {{val| 0 2 1 1 0 }}, {{val| 0 0 2 1 -3 }}]
+{{Mapping|legend=1| 1 1 1 2 5 | 0 2 1 1 0 | 0 0 2 1 -3 }}
-Mapping generators: ~2, ~49/40, ~10/7
 Mapping to lattice: [{{val| 0 2 1 1 0 }}, {{val| 0 0 2 1 -3 }}]
@@ Line 126: / Line 114: @@
 * [[11-odd-limit]]
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 23/10 3/10 2/5 0 -2/5 }}, {{monzo| 12/5 2/5 1/5 0 -1/5 }}, {{monzo| 23/10 3/10 -3/5 0 3/5 }}]
-: [[Eigenmonzo]]s (unchanged-intervals): 2, 4/3, 11/10
+: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.11/5
 {{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}
@@ Line 137: / Line 125: @@
 Comma list: 385/384, 625/624, 1375/1372
-Mapping: [{{val| 1 1 1 2 5 -1 }}, {{val| 0 2 1 1 0 2 }}, {{val| 0 0 2 1 -3 8 }}]
+Mapping: {{mapping| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }}
 {{Optimal ET sequence|legend=1| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }}
@@ Line 144: / Line 132: @@
 == Zisa ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 2401/2400, 5632/5625
-[[Mapping]]: [{{val| 1 1 1 2 -3 }}, {{val| 0 2 1 1 8 }}, {{val| 0 0 2 1 8 }}]
+{{Mapping|legend=1| 1 1 1 2 -3 | 0 2 1 1 8 | 0 0 2 1 8 }}
 {{Optimal ET sequence|legend=1| 31, 68e, 99e, 130, 239, 270, 670, 940, 1210, 2150c }}
@@ Line 159: / Line 147: @@
 Comma list: 1001/1000, 1716/1715, 4096/4095
-Mapping: [{{val| 1 1 1 2 -3 7 }}, {{val| 0 2 1 1 8 -6 }}, {{val| 0 0 2 1 8 -3 }}]
+Mapping: {{mapping| 1 1 1 2 -3 7 | 0 2 1 1 8 -6 | 0 0 2 1 8 -3 }}
 {{Optimal ET sequence|legend=1| 31, 78f, 99e, 109, 130, 239, 270, 571, 701, 841, 971, 1241 }}
@@ Line 166: / Line 154: @@
 == Baldur ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 2401/2400, 9801/9800
-[[Mapping]]: [{{val| 2 0 1 3 7 }}, {{val| 0 2 1 1 -2 }}, {{val| 0 0 2 1 3 }}]
+{{Mapping|legend=1| 2 0 1 3 7 | 0 2 1 1 -2 | 0 0 2 1 3 }}
-[[Mapping generator]]s: ~99/70, ~343/198, ~10/7
+: mapping generators: ~99/70, ~343/198, ~10/7
 [[Minimax tuning]]:
 * [[11-odd-limit]]
 : [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/4 0 1/2 1/2 -1/2 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 23/16 0 5/8 1/8 -1/8 }}, {{monzo| 23/16 0 5/8 -7/8 7/8 }}]
-: [[Eigenmonzo]]s (unchanged-intervals): 5/4, 14/11
+: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5.11/7
 {{Optimal ET sequence|legend=1| 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de }}
@@ Line 190: / Line 178: @@
 Comma list: 676/675, 1001/1000, 1716/1715
-Mapping: [{{val| 2 0 1 3 7 -1 }}, {{val| 0 2 1 1 -2 4 }}, {{val| 0 0 2 1 3 2 }}]
+Mapping: {{mapping| 2 0 1 3 7 -1 | 0 2 1 1 -2 4 | 0 0 2 1 3 2 }}
 {{Optimal ET sequence|legend=1| 58, 72, 130, 198, 270, 940, 1210f }}
@@ Line 201: / Line 189: @@
 == Freya ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 2401/2400, 3025/3024
-[[Mapping]]: [{{val| 1 1 3 3 2 }}, {{val| 0 2 3 2 1 }}, {{val| 0 0 -4 -2 3 }}]
+{{Mapping|legend=1| 1 1 3 3 2 | 0 2 3 2 1 | 0 0 -4 -2 3 }}
-Mapping generators: ~2, ~49/40, ~55/42
+: mapping generators: ~2, ~49/40, ~55/42
 [[Minimax tuning]]:
@@ Line 223: / Line 211: @@
 Comma list: 2401/2400, 3025/3024, 4096/4095
-Mapping: [{{val| 1 1 3 3 2 4 }}, {{val| 0 2 3 2 1 -9 }}, {{val| 0 0 -4 -2 3 6 }}]
+Mapping: {{mapping| 1 1 3 3 2 4 | 0 2 3 2 1 -9 | 0 0 -4 -2 3 6 }}
-Mapping generators: ~2, ~49/40, ~55/42
 {{Optimal ET sequence|legend=1| 31, 41, 72f, 198f, 229, 239, 270, 571, 581, 851, 882, 1152, 1463, 1733, 2615 }}
@@ Line 238: / Line 224: @@
 Comma list: 2080/2079, 2401/2400, 3025/3024
-Mapping: [{{val| 1 1 3 3 2 0 }}, {{val| 0 2 3 2 1 6 }}, {{val| 0 0 -4 -2 3 5 }}]
+Mapping: {{mapping| 1 1 3 3 2 0 | 0 2 3 2 1 6 | 0 0 -4 -2 3 5 }}
-Mapping generators: ~2, ~49/40, ~55/42
 {{Optimal ET sequence|legend=1| 13cdf, 31f, 41, 72, 157, 185cf, 198, 270, 581, 851, 1504, 1774f, 2085, 2355f }}
@@ Line 251: / Line 235: @@
 Comma list: 1225/1224, 2058/2057, 2080/2079, 2401/2400
-Mapping: [{{val| 1 1 3 3 2 0 7 }}, {{val| 0 2 3 2 1 6 6 }}, {{val| 0 0 -4 -2 3 5 -12 }}]
+Mapping: {{mapping| 1 1 3 3 2 0 7 | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 5 -12 }}
-Mapping generators: ~2, ~49/40, ~55/42
 {{Optimal ET sequence|legend=1| 41g, 72, 198g, 239f, 270, 311, 509, 581, 1234, 1815 }}
@@ Line 264: / Line 246: @@
 Comma list: 1225/1224, 1540/1539, 2080/2079, 3136/3135, 4200/4199
-Mapping: [{{val| 1 1 3 3 2 0 7 6 }}, {{val| 0 2 3 2 1 6 6 -2 }}, {{val| 0 0 -4 -2 3 5 -12 -3 }}]
+Mapping: {{mapping| 1 1 3 3 2 0 7 6 | 0 2 3 2 1 6 6 -2 | 0 0 -4 -2 3 5 -12 -3 }}
 Mapping generators: ~2, ~49/40, ~55/42
@@ Line 277: / Line 259: @@
 Comma list: 1001/1000, 1716/1715, 3025/3024
-Mapping: [{{val| 1 1 3 3 2 7 }}, {{val| 0 2 3 2 1 6 }}, {{val| 0 0 -4 -2 3 -13 }}]
+Mapping: {{mapping| 1 1 3 3 2 7 | 0 2 3 2 1 6 | 0 0 -4 -2 3 -13 }}
-Mapping generators: ~2, ~49/40, ~55/42
 {{Optimal ET sequence|legend=1| 8bcef, 15bbccdeeff, 23bcf, 31, 72, 103, 167, 198, 270, 571, 643, 913f }}
@@ Line 292: / Line 272: @@
 Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 1716/1715
-Mapping: [{{val| 1 1 3 3 2 7 7 }}, {{val| 0 2 3 2 1 6 6 }}, {{val| 0 0 -4 -2 3 -13 -12 }}]
+Mapping: {{mapping| 1 1 3 3 2 7 7 | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 -13 -12 }}
-Mapping generators: ~2, ~49/40, ~17/13
+: mapping generators: ~2, ~49/40, ~17/13
 {{Optimal ET sequence|legend=1| 8bcefg, 15bbccdeeffggg, 23bcfg, 31, 64be, 72, 103, 167, 198g, 239, 270 }}
@@ Line 301: / Line 281: @@
 == Vili ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 2401/2400, 391314/390625
-[[Mapping]]: [{{val| 1 1 5 4 10 }}, {{val| 0 2 3 2 6 }}, {{val| 0 0 -6 -3 -14 }}]
+{{Mapping|legend=1| 1 1 5 4 10 | 0 2 3 2 6 | 0 0 -6 -3 -14 }}
 {{Optimal ET sequence|legend=1| 27e, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 670, 913, 1043, 1313, 1583 }}
@@ Line 316: / Line 296: @@
 Comma list: 1001/1000, 1716/1715, 4225/4224
-Mapping: [{{val| 1 1 5 4 10 4 }}, {{val| 0 2 3 2 6 1 }}, {{val| 0 0 -6 -3 -14 -1 }}]
+Mapping: {{mapping| 1 1 5 4 10 4 | 0 2 3 2 6 1 | 0 0 -6 -3 -14 -1 }}
 {{Optimal ET sequence|legend=1| 27e, 37, 64be, 76e, 93, 103, 130, 233, 243e, 270, 643, 913f }}
@@ Line 323: / Line 303: @@
 == Frigg ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 2401/2400, 644204/643125
-[[Mapping]]: [{{val| 1 1 3 3 4 }}, {{val| 0 2 3 2 4 }}, {{val| 0 0 -10 -5 -11 }}]
+{{Mapping|legend=1| 1 1 3 3 4 | 0 2 3 2 4 | 0 0 -10 -5 -11 }}
 {{Optimal ET sequence|legend=1| 45e, 58, 103, 161, 212, 270, 643, 913, 1183e }}
@@ Line 338: / Line 318: @@
 Comma list: 1001/1000, 1716/1715, 10648/10647
-Mapping: [{{val| 1 1 3 3 4 5 }}, {{val| 0 2 3 2 4 3 }}, {{val| 0 0 -10 -5 -11 -14 }}]
+Mapping: {{mapping| 1 1 3 3 4 5 | 0 2 3 2 4 3 | 0 0 -10 -5 -11 -14 }}
 {{Optimal ET sequence|legend=1| 45ef, 58, 103, 161, 212, 270, 643, 913f, 1614ef }} <nowiki>*</nowiki>
@@ Line 347: / Line 327: @@
 == Ennealimmic ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 2401/2400, 4375/4374
-[[Mapping]]: [{{val| 9 1 1 12 0 }}, {{val| 0 2 3 2 0 }}, {{val| 0 0 0 0 1 }}]
+{{Mapping|legend=1| 9 1 1 12 0 | 0 2 3 2 0 | 0 0 0 0 1 }}
-Mapping generators: 27/25, 5/3, 11
+: mapping generators: ~27/25, ~5/3, ~11
 {{Optimal ET sequence|legend=1| 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd }}
@@ Line 364: / Line 344: @@
 Comma list: 2080/2079, 2401/2400, 4375/4374
-Mapping: [{{val| 9 1 1 12 0 -31 }}, {{val| 0 2 3 2 0 5 }}, {{val| 0 0 0 0 1 1 }}]
+Mapping: {{mapping| 9 1 1 12 0 -31 | 0 2 3 2 0 5 | 0 0 0 0 1 1 }}
 {{Optimal ET sequence|legend=1| 27, 45f, 54cff, 72, 171, 198, 270, 639, 711, 981, 1692e }}
@@ Line 372: / Line 352: @@
 [[Category:Temperament families]]
 [[Category:Breed family| ]] <!-- main article -->
+[[Category:Breed| ]] <!-- key article -->
 [[Category:Rank 3]]

Breed family: Difference between revisions

Revision as of 05:39, 15 September 2023

Breed

Jove

Jovial

17-limit

Jofur

Jovis

Agni

13-limit

Zisa

13-limit

Baldur

Greenland

Freya

13-limit

Eir

17-limit

19-limit

Heimlaug

17-limit

Vili

13-limit

Frigg

13-limit

Ennealimmic

13-limit

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